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General Reference: "I belong in London" means "I am naturally suited to London, and it's best I should be there". If you belong to something/someone, you're owned, and must perforce do whatever something/someone dictates.
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FumbleFingersJun 19 '12 at 17:11

Although I think it's General Reference and should be closed anyway, +1 for being short & to the point, with a really slick example!
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FumbleFingersJun 19 '12 at 21:00

Indeed, it is fairly generic. Preposition questions, though, are very important. FumbleFingers has a good point about the conciseness, as well, as mine turned out to read like some saga, in addition to being loaded with speculation.
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shinyspoongodJun 19 '12 at 21:05

Thank you for the up-vote and compliment. I explained the point in a very simple manner, I'm glad that it explains the point clearly.
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Fr0zenFyrJun 20 '12 at 2:30

To me the phrase "I belong in this world" most likely fits with someone who was disillusioned with the way things were going, and is somehow finding a way to get on their feet again. Something like, "This place really is home" or "If I have to work here I may as well identify with something of the place" It may well describe that the person no longer feels out of place, or out of touch, with the surrounding environment. I hope you don't mind that this is quite a speculative interpretation.

The general meaning is essentially as @Fr0zenFyr described it, in that belonging to something is already having the bonds to it, and belonging in something is having a purpose or destiny in that environment, whether that be a team or workplace, or whatever else.

Another example: "He belongs to the local militia, but with his training he belongs in the national army." would be a way of stating that his membership in the local militia is existent, but that he should leave and go the national army.